This paper states, proves, and closes the Persistence Admissibility Theorem (PAT) and establishes the structural unavoidability of La Profilée. It supersedes Papers 81 v1/v2 and incorporates Paper 82 (Admissibility Necessity), closing all previously open precision points. Version 2 incorporates five reviewer-hardening additions to the original P103 argument: (1) explicit proof that F, M, K are not re-labelings but the irreducible logical invariants of any persistence verdict; (2) clarification that the classification into three transformation structures is structural and non-evaluative, not presupposing M3; (3) the functional class exhaustion proof establishing multiplicativity as the only form in the admissible class, not merely the unique representative; (4) the separation of universality from empirical coverage; (5) the residual condition argument establishing that IR ≤ 1 is not a tautology but the result of eliminative closure. Part I (Sections 1–5): PAT — within the full admissibility class C defined by Conditions 1–7, the unique global persistence condition is R ≤ F·M·K. Key improvements over v1: Sub-Lemma 2.1 formally derives countable order-density from Condition 4; Lemma 4 closes the triadic architecture through Q1–Q3 exhaustion and B1–B4 exclusion; the C₀→C₁ transition is established internally; C3 is proved as a structural consequence of C1+C2, not an independent axiom. Part II (Sections 6–9): Unavoidability — F, M, K are logical invariants of any possible persistence verdict, not variables introduced into a model. The admissibility class C is not assumed — it is induced. LP is not derived from persistence theories. Persistence theories are constrained projections of LP.
Marc Maibom (Sun,) studied this question.